How can I set edges to a specific length with the keyboard?
No, you just cannot set the edge length by typing a number. I don't know why Blender does not add this feature, it's just stupid. 

--Edit--

Just found an Add-on
https://developer.blender.org/T39999  After putting the .py file into your addons folder you can just use Shift-Alt-E to set the edge length